Queensland Roar coach Frank Farina has been fined by Football Federation Australia (FFA) for his criticism of the referee after his side's Round 19 loss to Melbourne Victory.

The FFA said it had fined the former Socceroos coach an undisclosed amount - understood to be $2,000 - for breaching the A-League's code of conduct.

Following the Roar's 2-1 loss to the Victory at Suncorp Stadium on January 5, Farina questioned why referee Matthew Breeze did not award a penalty when a shot from striker Simon Lynch struck the arm of the Victory's Kevin Muscat.

"Apparently the referee said it wasn't intentional," Farina said in the post-match media conference.

"Well I think we'll have to get them to look at the rule book because intentional or not, the shot was goal-bound and it clearly struck him on the arm."

The Roar sent a letter to the FFA explaining Farina's position when the club was made aware of the possible disciplinary action last week, but that did not sway the governing body.

An appeal of the fine appears unlikely.

Farina did not comment on the matter at training, but in the post-match media conference following his side's 0-0 draw with Sydney FC in Brisbane on Sunday he issued a pre-emptive apology to journalists for not answering questions about officials.

"Don't think it's against you guys if I can't answer some things," Farina told reporters.

"Unless you ask me questions which are nice and I can only give nice answers, please don't bother."